scholarly journals Graceful Labeling of Hypertrees

2021 ◽  
Vol 13 (1) ◽  
pp. 28
Author(s):  
H. El-Zohny ◽  
S. Radwan ◽  
S.I. Abo El-Fotooh ◽  
Z. Mohammed
Keyword(s):  
Graph Theory ◽  
Simple Graph ◽  
Graph Labeling ◽  
Graceful Labeling ◽  
Edge Labeling

Graph labeling is considered as one of the most interesting areas in graph theory. A labeling for a simple graph G (numbering or valuation), is an association of non -negative integers to vertices of G  (vertex labeling) or to edges of G  (edge labeling) or both of them. In this paper we study the graceful labeling for the k- uniform hypertree and define a condition for the corresponding tree to be graceful. A k- uniform hypertree is graceful if the minimum difference of vertices’ labels of each edge is distinct and each one is the label of the corresponding edge.

scholarly journals Tree-Antimagicness of Web Graphs and Their Disjoint Union

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Zhijun Zhang ◽  
Muhammad Awais Umar ◽  
Xiaojun Ren ◽  
Basharat Rehman Ali ◽  
Mujtaba Hussain ◽  
...  
Keyword(s):  
Graph Theory ◽  
Disjoint Union ◽  
Graph Labeling ◽  
Labeled Graph ◽  
Antimagic Labeling ◽  
Research Article ◽  
Web Graphs ◽  
Vertex Set ◽  
Edge Labeling

In graph theory, the graph labeling is the assignment of labels (represented by integers) to edges and/or vertices of a graph. For a graph G=V,E, with vertex set V and edge set E, a function from V to a set of labels is called a vertex labeling of a graph, and the graph with such a function defined is called a vertex-labeled graph. Similarly, an edge labeling is a function of E to a set of labels, and in this case, the graph is called an edge-labeled graph. In this research article, we focused on studying super ad,d-T4,2-antimagic labeling of web graphs W2,n and isomorphic copies of their disjoint union.

scholarly journals Cryptosystem using double vertex graph

2020 ◽  
Vol 13 (44) ◽  
pp. 4483-4489
Author(s):  
C Beaula ◽  
Keyword(s):  
Graph Theory ◽  
Secure Communication ◽  
System Method ◽  
Encryption And Decryption ◽  
Vertex Graph ◽  
Private And Public ◽  
Almost All ◽  
Encryption Method ◽  
The Given ◽  
Edge Labeling

Background/Objective: The Coronavirus Covid-19 has affected almost all the countries and millions of people got infected and more deaths have been reported everywhere. The uncertainty and fear created by the pandemic can be used by hackers to steal the data from both private and public systems. Hence, there is an urgent need to improve the security of the systems. This can be done only by building a strong cryptosystem. So many researchers started embedding different topics of mathematics like algebra, number theory, and so on in cryptography to keep the system, safe and secure. In this study, a cryptosystem using graph theory has been attempted, to strengthen the security of the system. Method: A new graph is constructed from the given graph, known as a double vertex graph. The edge labeling of this double vertex graph is used in encryption and decryption. Findings: A new cryptosystem using the amalgamation of the path, its double vertex graph and edge labeling has been proposed. From the double vertex graph of a path, we have given a method to find the original path. To hack such an encrypted key, the knowledge of graph theory is important, which makes the system stronger. Applications:The one-word encryption method will be useful in every security system that needs a password for secure communication or storage or authentication. Keywords: Double vertex graphs; path; adjacency matrix; encryption; cryptography

scholarly journals Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yajing Wang ◽  
Yubin Gao
Keyword(s):  
Graph Theory ◽  
Spectral Radius ◽  
Adjacency Matrix ◽  
Upper Bounds ◽  
Simple Graph ◽  
Spectral Graph Theory ◽  
Extremal Graphs ◽  
Spectral Graph ◽  
Vertex Set

Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

scholarly journals Applications of mathematical programming in graceful labeling of graphs

2004 ◽  
Vol 2004 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Kourosh Eshghi ◽  
Parham Azimi
Keyword(s):  
Mathematical Programming ◽  
Graph Labeling ◽  
Computational Results ◽  
Programming Technique ◽  
New Approach ◽  
Graceful Labeling ◽  
Applications Of Mathematical Programming ◽  
The Subject ◽  
Mathematical Programming Technique ◽  
Special Classes

Graceful labeling is one of the best known labeling methods of graphs. Despite the large number of papers published on the subject of graph labeling, there are few particular techniques to be used by researchers to gracefully label graphs. In this paper, first a new approach based on the mathematical programming technique is presented to model the graceful labeling problem. Then a “branching method” is developed to solve the problem for special classes of graphs. Computational results show the efficiency of the proposed algorithm for different classes of graphs. One of the interesting results of our model is in the class of trees. The largest tree known to be graceful has at most 27 vertices but our model can easily solve the graceful labeling for trees with 40 vertices.

On Edge-Balance Index Sets of the Graph CnxP6(n=3,4,5mod6)

2011 ◽  
Vol 339 ◽  
pp. 662-665
Author(s):  
Yu Rong Ji ◽  
Ai Jun Li ◽  
Jing Jing Yao
Keyword(s):  
Simple Graph ◽  
Index Sets ◽  
Vertex Set ◽  
Binary Edge ◽  
Balance Index ◽  
Edge Labeling

Let G be a simple graph with vertex set V(G) and edge set E(G), and let Z2 = {0,1}. For a given binary edge labeling f :E(G)→Z2 , the edge labeling f induces a partial vertex labeling f*:V(G)→Z2 such that f*(v) =1(0) iff the number of 1-edges (0-edges) is strictly greater than the number of 0-edges (1-edges) incident to v , otherwise f*(v) is idefined. For i∈Z2 , let v(i)=card{v∈V(G): f*(v) =i} and e(i) = card{e∈E(G) : f (e)=i}. The edge-balance index sets of a graph G,EBI(G), is defined as {|v(0) −v(1) |: the edge labeling f satisfies |e(0)−e(1) |≤1}.In this paper, we completely determine the edge-balance CnxP 6(n=3,4,5mod6).

scholarly journals Medicinal cupping in the eyes of graph theory

2020 ◽  
Vol 1 (01) ◽  
pp. 44-49
Author(s):  
N.M Hanafi ◽  
Y. Yusof ◽  
M.S. Mohamad ◽  
M.F.A Bakar ◽  
M.A. Ibrahim
Keyword(s):  
Graph Theory ◽  
Human Health ◽  
Healing Process ◽  
Optimal Number ◽  
Simple Graph ◽  
The Body ◽  
Graph Colouring ◽  
Traditional Treatment ◽  
The World ◽  
Definition Of

Medicinal cupping is one of the traditional treatment methods that is trusted to give many benefits to the human health and still practising by various culture and societies around the world. The purposes of this treatment are to allow the toxin leaves the body,to stimulate the muscles and also helping in healing process for various diseases. The process start by placing special heated cups on specific points to create suction, then the points will be punctured. Each disease has specific cupping points to be cupped which located on the human nerves system. All the points actually connected to each other where a simple graph can be formed. Since there are limited studies that discuss medicinal cupping in a mathematics view, thus this research is conducted to introduce the easiest way  on demonstrating the cupping points on the human nerves system by using the idea of graph. Hence, new definition of nerve vertex, nerve edge and nerve graph will be defined. Moreover, the idea of graph colouring will be applied to determine the optimal number of cupping points.

scholarly journals Vertex Antimagic Edge Labeling of Cube of a Path Graph

2019 ◽  
Vol 9 (2) ◽  
pp. 1952-1955
Keyword(s):  
Graph Theory ◽  
Graph Theoretic ◽  
Path Graph ◽  
Different Types ◽  
Different Characteristics ◽  
Edge Labeling

There are many concepts in science that are very hard to understand and to make use of them in a effective way, it is atmost important to have a tool that best explains these complex concepts in a simpler way. Graph theory is one of the most interesting topics in mathematics that was used to explain many complicated concepts in a simpler and easier way. Graph theory is not just about points and lines and above all, there are many interesting topics in graph theory which has motivated many scholars to pursue research in different areas. One of the most interesting and elite topics in graph theory is the path. The researchers have discovered different types of concepts using paths and have proved different characteristics. Cube of a path graphs are one of those fascinating graphs that have evolved from paths and has been proved to admit a variety of properties. Like paths, labeling is also an area where graph theoretic researchers have shown great interest and have come up with different types of labeling. With the discovery of a spate of labeling, it has motivated and kindled the researchers to apply these labeling to a variety of graphs and check the admittance of different types of properties. One such intriguing type of labeling is the vertex antimagic edge labeling. In this paper, we will show that the cube of a path graph admits vertex antimagic edge labeling.

scholarly journals A variant of Niessen’s problem on degreesequences of graphs

2014 ◽  
Vol Vol. 16 no. 1 (Graph Theory) ◽  
Author(s):  
Jiyun Guo ◽  
Jianhua Yin
Keyword(s):  
Graph Theory ◽  
Discrete Math ◽  
Simple Graph ◽  
The Other ◽  
Degree Sequences ◽  
International Audience

Graph Theory International audience Let (a1,a2,\textellipsis,an) and (b1,b2,\textellipsis,bn) be two sequences of nonnegative integers satisfying the condition that b1>=b2>=...>=bn, ai<= bi for i=1,2,\textellipsis,n and ai+bi>=ai+1+bi+1 for i=1,2,\textellipsis, n-1. In this paper, we give two different conditions, one of which is sufficient and the other one necessary, for the sequences (a1,a2,\textellipsis,an) and (b1,b2,\textellipsis,bn) such that for every (c1,c2,\textellipsis,cn) with ai<=ci<=bi for i=1,2,\textellipsis,n and &#x2211;&limits;i=1n ci=0 (mod 2), there exists a simple graph G with vertices v1,v2,\textellipsis,vn such that dG(vi)=ci for i=1,2,\textellipsis,n. This is a variant of Niessen\textquoterights problem on degree sequences of graphs (Discrete Math., 191 (1998), 247&#x2013;253).

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